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Identification and Empirical Likelihood Inference in Nonlinear Regression Model with Nonignorable Nonresponse

Author

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  • Xianwen Ding

    (Department of Statistics, Jiangsu University of Technology, Changzhou 213001, China)

  • Xiaoxia Li

    (School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China)

Abstract

The identification of model parameters is a central challenge in the analysis of nonignorable nonresponse data. In this paper, we propose a novel penalized semiparametric likelihood method to obtain sparse estimators for a parametric nonresponse mechanism model. Based on these sparse estimators, an instrumental variable is introduced, enabling the identification of the observed likelihood. Two classes of estimating equations for the nonlinear regression model are constructed, and the empirical likelihood approach is employed to make inferences about the model parameters. The oracle properties of the sparse estimators in the nonresponse mechanism model are systematically established. Furthermore, the asymptotic normality of the maximum empirical likelihood estimators is derived. It is also shown that the empirical log-likelihood ratio functions are asymptotically weighted chi-squared distributed. Simulation studies are conducted to validate the effectiveness of the proposed estimation procedure. Finally, the practical utility of our approach is demonstrated through the analysis of ACTG 175 data.

Suggested Citation

  • Xianwen Ding & Xiaoxia Li, 2025. "Identification and Empirical Likelihood Inference in Nonlinear Regression Model with Nonignorable Nonresponse," Mathematics, MDPI, vol. 13(9), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1388-:d:1641624
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    References listed on IDEAS

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    1. Wang Miao & Eric J. Tchetgen Tchetgen, 2016. "On varieties of doubly robust estimators under missingness not at random with a shadow variable," Biometrika, Biometrika Trust, vol. 103(2), pages 475-482.
    2. Tianqing Liu & Xiaohui Yuan, 2020. "Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data," Statistical Papers, Springer, vol. 61(6), pages 2241-2270, December.
    3. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    4. Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Sima Sharghi & Kevin Stoll & Wei Ning, 2024. "Statistical inferences for missing response problems based on modified empirical likelihood," Statistical Papers, Springer, vol. 65(7), pages 4079-4120, September.
    7. Zhou, Yong & Wan, Alan T. K & Wang, Xiaojing, 2008. "Estimating Equations Inference With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1187-1199.
    8. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    9. Liugen Xue & Junshan Xie, 2024. "Efficient robust estimation for single-index mixed effects models with missing observations," Statistical Papers, Springer, vol. 65(2), pages 827-864, April.
    10. Kenji Beppu & Kosuke Morikawa, 2024. "Verifiable identification condition for nonignorable nonresponse data with categorical instrumental variables," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 8(1), pages 40-50, January.
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